content stringlengths 0 625k | subset stringclasses 1
value | meta dict |
|---|---|---|
---
abstract: |
Let $X$ and $t$ be real numbers, $X\ge 1$ and $t>1$. The family of sets $$\left\{\left\lfloor \frac{X}{n^t} \right\rfloor ~:~ 1\leq n\leq X\right\}$$ are very sparse sets that satisfy the prime number theorem as $X$ increases. We give an exact formula for the cardinality of these sets.
author:
- "[RAN... | arxiv_math | {
"id": "2309.16072",
"title": "An exact formula for a family of floor function sets",
"authors": "Randell Heyman and MD Rahil Miraj",
"categories": "math.NT",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0/"
} |
---
abstract: |
The anti-Ramsey number $\mathrm{ar}(n,F)$ of an $r$-graph $F$ is the minimum number of colors needed to color the complete $n$-vertex $r$-graph to ensure the existence of a rainbow copy of $F$. We prove a general upper bound for $\mathrm{ar}(n,F)$ when $F$ is the expansion of a hypergraph with smaller... | arxiv_math | {
"id": "2310.01186",
"title": "Hypergraph anti-Ramsey theorems",
"authors": "Xizhi Liu and Jialei Song",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by-nc-sa/4.0/"
} |
---
abstract: |
The representation theory of a commutative noetherian ring is tightly controlled by its prime spectrum. In this article we use the prime spectrum to describe mutation of cosilting objects in the derived category of a commutative noetherian ring.
address: Jorge Vitória, Dipartimento di Matematica "Tull... | arxiv_math | {
"id": "2310.01834",
"title": "Mutations and derived equivalences for commutative noetherian rings",
"authors": "Jorge Vit\\'oria",
"categories": "math.RT math.AC math.RA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
author:
- |
Hazhe Ye, Yingzhi Tian[^1]\
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China
title: "Characterizing the forbidden pairs for graphs to be super-edge-connected[^2]"
---
GBKsong
Let $\mathcal{H}$ be a set of given connected graphs. A graph $G$ is said to... | arxiv_math | {
"id": "2309.00829",
"title": "Characterizing the forbidden pairs for graphs to be super-edge-connected",
"authors": "Hazhe Ye, Yingzhi Tian",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
The *echo index* counts the number of simultaneously stable asymptotic responses of a nonautonomous (i.e. input-driven) dynamical system. It generalizes the well-known *echo state property* for recurrent neural networks - this corresponds to the echo index being equal to one. In this paper, we investi... | arxiv_math | {
"id": "2309.04728",
"title": "Transitions in echo index and dependence on input repetitions",
"authors": "Peter Ashwin and Andrea Ceni",
"categories": "math.DS cs.AI cs.LG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We investigate the distortion of the Assouad dimension and (regularized) spectrum of sets under planar quasiregular maps. While the respective results for the Hausdorff and upper box-counting dimension follow immediately from their quasiconformal counterparts by employing elementary properties of thes... | arxiv_math | {
"id": "2309.07362",
"title": "Quasiregular distortion of dimensions",
"authors": "Efstathios Konstantinos Chrontsios Garitsis",
"categories": "math.CV math.DS",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem for history dependent operators, results on the well-posednes... | arxiv_math | {
"id": "2309.06516",
"title": "Well-posedness of Constrained Evolutionary Differential\n Variational-Hemivariational Inequalities",
"authors": "S. Migorski",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper, we work with the existence and uniqueness of free boundary constant mean curvature hypersurfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. Under some conditions on the function that generates the graph and a gap condition on the umbil... | arxiv_math | {
"id": "2309.10405",
"title": "Gap results and existence of CMC free boundary hypersurfaces in\n rotational domains",
"authors": "Allan Freitas, M\\'arcio Santos, and J. Sindeaux",
"categories": "math.DG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this article, we point out the connections between the distinguished varieties introduced by Agler and McCarthy with certain uniform algebras on bidisc studied by Samuelsson and Wold. We also prove analogues of Samuelsson-Wold result for the domains in $\mathbb{C}^2$ that are the images of the bidi... | arxiv_math | {
"id": "2309.05006",
"title": "Uniform algebras and distinguished varieties",
"authors": "Sushil Gorai, Golam Mostafa Mondal",
"categories": "math.CV",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We discuss a central limit theorem in the framework of the group algebra of the Thompson group $F$. We consider the sequence of self-adjoint elements given by $a_n=\frac{g_n+g_n^{*}}{\sqrt{2}}$ in the noncommutative probability space $( {\mathbb{C}} (F),\varphi)$, where the expectation functional $\va... | arxiv_math | {
"id": "2309.05626",
"title": "A central limit theorem in the framework of the Thompson group $F$",
"authors": "Arundhathi Krishnan",
"categories": "math.OA math.CO math.GR math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
---
Research highlight 1
Research highlight 2
#
00
| arxiv_math | {
"id": "2309.02431",
"title": "Crack propagation in anisotropic brittle materials: from a phase-field\n model to a shape optimization approach",
"authors": "Tim Suchan, Chaitanya Kandekar, Wolfgang E. Weber, Kathrin Welker",
"categories": "math.OC",
"license": "http://arxiv.org/licenses/nonexclusive-distrib... |
---
abstract: |
The special shadow-complexity is an invariant of closed $4$-manifolds defined by Costantino using Turaev's shadows. We show that for any positive integer $k$, the special shadow-complexity of the connected sum of $k$ copies of $S^1\times S^3$ is exactly $k+1$.
address: Department of Mathematics, Chuo... | arxiv_math | {
"id": "2309.09225",
"title": "The special shadow-complexity of $\\#_k(S^1\\times S^3)$",
"authors": "Hironobu Naoe",
"categories": "math.GT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this note, we establish a bi-parameter linear localization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing.
address:
- |
Jingyu Huang\
School of Mathematics\
Watson Building\
University of Birmingham\
Edgbaston\
Birmingham\
B15 2TT\... | arxiv_math | {
"id": "2309.16506",
"title": "On the linear localization of the one-dimensional stochastic wave\n equation with a multiplicative space-time white noise forcing",
"authors": "Jingyu Huang, Tadahiro Oh, and Mamoru Okamoto",
"categories": "math.AP math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-d... |
---
abstract: |
Let $E=\mathbb{Q}\big(\sqrt{-d}\big)$ be an imaginary quadratic field for a square-free positive integer $d$, and let $\mathcal{O}$ be its ring of integers. For each positive integer $m$, let $I_m$ be the free Hermitian lattice over $\mathcal{O}$ with an orthonormal basis, let $\mathfrak{S}_d(1)$ be t... | arxiv_math | {
"id": "2309.16138",
"title": "An algorithm for $g$-invariant on unary Hermitian lattices over\n imaginary quadratic fields",
"authors": "Jingbo Liu",
"categories": "math.NT cs.DS",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper, we obtain a classification theorem of $2$-dimensional complete Lagrangian self-expanders with constant squared norm of the second fundamental form in $\mathbb C^{2}$.
address:
- |
Zhi Li\
College of Mathematics and Information Science, Henan Normal University, , Xinxiang, Henan, Chi... | arxiv_math | {
"id": "2309.16324",
"title": "Complete lagrangian self-expanders in $\\mathbb C^{2}$",
"authors": "Zhi Li and Guoxin Wei",
"categories": "math.DG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Let $\mu$ and $\nu$ be compactly supported probability measures on the real line with densities with respect to Lebesgue measure. We show that for all large real $z$, if $\mu \boxplus \nu$ is their additive free convolution, we have $$\int_{-\infty}^\infty \log(z - x) \mu \boxplus \nu (\mathrm{d}x) = ... | arxiv_math | {
"id": "2309.12196",
"title": "A variational approach to free probability",
"authors": "Octavio Arizmendi and Samuel G. G. Johnston",
"categories": "math.PR math.FA math.OA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Let $L$ be an even lattice of odd rank with discriminant group $L'/L$, and let $\alpha,\beta \in L'/L$. We prove the Weil bound for the Kloosterman sums $S_{\alpha,\beta}(m,n,c)$ of half-integral weight for the Weil Representation attached to $L$. We obtain this bound by proving an identity that relat... | arxiv_math | {
"id": "2309.08528",
"title": "The Weil bound for generalized Kloosterman sums of half-integral weight",
"authors": "Nickolas Andersen, Gradin Anderson, Amy Woodall",
"categories": "math.NT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
By a theorem of D. Wigner, an irreducible unitary representation with non-zero $(\frak{g},K)$-cohomology has trivial infinitesimal character, and hence up to unitary equivalence, these are finite in number. We have determined the number of equivalence classes of these representations and the Poincaré ... | arxiv_math | {
"id": "2309.12703",
"title": "Irreducible unitary representations with non-zero relative Lie algebra\n cohomology of the Lie group $SO_0(2,m)$",
"authors": "Ankita Pal, Pampa Paul",
"categories": "math.RT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
author:
- Kaushik Bal and Sanjit Biswas
bibliography:
- ref1.bib
nocite: "[@*]"
title: Semilinear degenerate elliptic equation in the presence of singular nonlinearity
---
# ABSTRACT {#abstract .unnumbered}
Given $\Omega(\subseteq\mathbb{R}^{1+m})$, a smooth bounded domain and a nonnegative measurable function $f... | arxiv_math | {
"id": "2309.04857",
"title": "Semilinear degenerate elliptic equation in the presence of singular\n nonlinearity",
"authors": "Kaushik Bal and Sanjit Biswas",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a parabolic subgroup of $\mathbb{G}$ with abelian unipotent radical.... | arxiv_math | {
"id": "2310.04839",
"title": "Clifford algebras, symmetric spaces and cohomology rings of\n Grassmannians",
"authors": "Kieran Calvert, Kyo Nishiyama, Pavle Pand\\v{z}i\\'c",
"categories": "math.RT math.DG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We study in detail the operad controlling several pre-Lie algebra structures sharing the same Lie bracket. Specifically, we show that this operad admits a combinatorial description similar to that of Chapoton and Livernet for the pre-Lie operad, and that it has many of the remarkable algebraic propert... | arxiv_math | {
"id": "2309.05552",
"title": "Combinatorics of pre-Lie products sharing a Lie bracket",
"authors": "Paul Laubie",
"categories": "math.QA math.CO math.RA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
A methodology for defining variational principles for a class of PDE models from continuum mechanics is demonstrated, and some of its features explored. The scheme is applied to quasi-static and dynamic models of rate-independent and rate-dependent, single crystal plasticity at finite deformation.
aut... | arxiv_math | {
"id": "2310.03201",
"title": "A Hidden Convexity in Continuum Mechanics, with application to\n classical, continuous-time, rate-(in)dependent plasticity",
"authors": "Amit Acharya",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Mixed volumes in $n$-dimensional Euclidean space are functionals of $n$-tuples consisting of convex bodies $K,L,C_1,\ldots,C_{n-2}$. The Alexandrov--Fenchel inequalities are fundamental inequalities between mixed volumes of convex bodies, which cover as very special cases many important inequalities b... | arxiv_math | {
"id": "2309.16864",
"title": "Extremizers of the Alexandrov--Fenchel inequality within a new class of\n convex bodies",
"authors": "Daniel Hug and Paul A. Reichert",
"categories": "math.MG",
"license": "http://creativecommons.org/licenses/by-nc-sa/4.0/"
} |
---
abstract: |
0.9 In 2005, Borisov and Sapir proved that ascending HNN extensions of finitely generated linear groups are residually finite. Subsequently, Druu and Sapir noted the existence of finitely generated non-linear residually finite groups based on the work of Borisov and Sapir. In 2017, Kharlampovich, Myas... | arxiv_math | {
"id": "2309.13389",
"title": "Non-linear, solvable, residually $p$ groups",
"authors": "Donsung Lee",
"categories": "math.GR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
This paper discusses parabolic reverse Hölder inequalities and their connections to parabolic Muckenhoupt weights. The main result gives several characterizations for this class of weights. There are challenging features related to the parabolic geometry and the time lag, for example, in covering and ... | arxiv_math | {
"id": "2310.00370",
"title": "Characterizations of parabolic reverse H\\\"older classes",
"authors": "Juha Kinnunen and Kim Myyryl\\\"ainen",
"categories": "math.CA math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper, we study solutions for a weakly coupled system of eikonal equations arising in an optimal path-planning problem for autonomous vehicles. The model considered takes into account the possibility of two types of breakdown, partial and total, which happen at a known, spatially inhomogeneous... | arxiv_math | {
"id": "2310.02966",
"title": "Weakly coupled systems of eikonal equations for autonomous vehicles",
"authors": "Maria Teresa Chiri and Kenneth D Czuprynski and Ludmil T Zikatanov",
"categories": "math.OC",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the given reference values of system outputs at each stage, we de... | arxiv_math | {
"id": "2309.13628",
"title": "Semidefinite Programming Approximation for a Matrix Optimization Problem\n over an Uncertain Linear System",
"authors": "Jintao Xu, Shu-Cherng Fang, Wenxun Xing",
"categories": "math.OC",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In 1976, Donald Cartwright and John McMullen characterized axiomatically the Riemann-Liouvile fractional integral in their paper [@CarMc], that was published in 1978. The motivation for their work was to answer affirmatively to a conjecture stated by J. S. Lew a few years before, in 1972. Essentially,... | arxiv_math | {
"id": "2309.07148",
"title": "An extension of the Cartwright-McMullen theorem in fractional calculus\n for the smooth Stieltjes case",
"authors": "Daniel Cao Labora",
"categories": "math.CA math.FA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Let $A(p,n,k)$ denote the number of $p$-tuples of commuting permutations of $n$ elements whose permutation action results in exactly $k$ orbits or connected components. We provide a new proof of an explicit formula for $A(p,n,k)$ which is essentially due to Bryan and Fulman, in their work on orbifold ... | arxiv_math | {
"id": "2309.09407",
"title": "A bijection for tuples of commuting permutations and a log-concavity\n conjecture",
"authors": "Abdelmalek Abdesselam, Pedro Brunialti, Tristan Doan, Philip Velie",
"categories": "math.CO math.NT math.PR",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
# Deformations of $\nabla$-Parallel Spinors {#section:canonically_parallel}
In this section we study solutions of the equation $\nabla \psi =0$ on a $\tad$ manifold, and describe how they change under $\mathcal{H}$-homothetic deformations. It is known from [@3str Cor.4.1.1] that the $\nabla$-holonomy algebra satisfies... | arxiv_math | {
"id": "2309.16610",
"title": "$\\mathcal{H}$-Killing Spinors and Spinorial Duality for Homogeneous\n 3-$(\\alpha,\\delta)$-Sasaki Manifolds",
"authors": "Ilka Agricola and Jordan Hofmann",
"categories": "math.DG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this expository paper we discuss several properties on closed aspherical parabolic ${{\mathsf{G}}}$-manifolds $X/\Gamma$. These are manifolds $X/\Gamma$, where $X$ is a smooth contractible manifold with a parabolic ${{\mathsf{G}}}$-structure for which $\Gamma\leq \mathop{\rm Aut}\nolimits_{{\mathsf... | arxiv_math | {
"id": "2309.13569",
"title": "On the automorphism group of parabolic structures and closed aspherical\n manifolds",
"authors": "Oliver Baues and Yoshinobu Kamishima",
"categories": "math.DG math.GT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper, we study subgroup separability (also known as LERF) and related properties for surface braid groups and virtual (singular) braid groups
author:
- |
KISNNEY ALMEIDA\
Universidade Estadual de Feira de Santana,\
Departamento de Ciências Exatas,\
Av. Transnordestina S/N, CEP 44036-9... | arxiv_math | {
"id": "2310.00478",
"title": "Subgroup separability of surface braid groups and virtual braid groups",
"authors": "Kisnney Almeida, Igor Lima, Oscar Ocampo",
"categories": "math.GR math.GT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
arxiv_math | {
"id": "2309.15058",
"title": "Monoidal Structures in Orthogonal Calculus",
"authors": "Leon Hendrian",
"categories": "math.AT",
"license": "http://creativecommons.org/licenses/by-sa/4.0/"
} | |
---
abstract: |
Let $\mathfrak{g}$ be an affine Lie algebra with associated Yangian $Y_\hbar(\mathfrak{g})$. We prove the existence of two meromorphic $R$--matrices associated to any pair of representations of $Y_\hbar(\mathfrak{g})$ in the category $\mathcal{O}$. They are related by a unitary constraint and construc... | arxiv_math | {
"id": "2309.02377",
"title": "The R-matrix of the affine Yangian",
"authors": "Andrea Appel, Sachin Gautam, Curtis Wendlandt",
"categories": "math.RT math-ph math.MP math.QA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We consider branching Brownian motion in which initially there is one particle at $x$, particles produce a random number of offspring with mean $m+1$ at the time of branching events, and each particle branches at rate $\beta = 1/2m$. Particles independently move according to Brownian motion with drift... | arxiv_math | {
"id": "2310.00707",
"title": "The all-time maximum for branching Brownian motion with absorption\n conditioned on long-time survival",
"authors": "Pascal Maillard and Jason Schweinsberg",
"categories": "math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
author:
- Guillaume Rialland
date: |
Université de Paris-Saclay, UVSQ, CNRS, Laboratoire de Mathématiques de Versailles, 78000 Versailles\
`guillaume.rialland@uvsq.fr`
title: "**Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes**"
---
... | arxiv_math | {
"id": "2310.01019",
"title": "Asymptotic stability of solitary waves for the 1D near-cubic non-linear\n Schr\\\"odinger equation in the absence of internal modes",
"authors": "Guillaume Rialland",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We study two coupled systems, one playing the role of the driver system and the other one of the driven system. The driver system is a time-delayed oscillator, and the driven or response system has a negligible delay. Since the driver system plays the role of the only external forcing of the driven sy... | arxiv_math | {
"id": "2309.07512",
"title": "Nonlinear delayed forcing drives a non-delayed Duffing oscillator",
"authors": "Mattia Coccolo, Miguel A.F. Sanju\\'an",
"categories": "math.DS math-ph math.MP nlin.CD",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
The pseudoforest version of the Strong Nine Dragon Tree Conjecture states that if a graph $G$ has maximum average degree $mad(G) = 2 \max_{H \subseteq G} \frac{e(G)}{v(G)}$ at most $2(k + \frac{d}{d+k+1})$, then it has a decomposition into $k+1$ pseudoforests where in one pseudoforest $F$ the componen... | arxiv_math | {
"id": "2310.00931",
"title": "Beyond the Pseudoforest Strong Nine Dragon Tree Theorem",
"authors": "Sebastian Mies, Benjamin Moore, and Evelyne Smith Roberge",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in strategic classification. We consider a state-dependent setti... | arxiv_math | {
"id": "2310.05792",
"title": "Two-timescale Derivative Free Optimization for Performative Prediction\n with Markovian Data",
"authors": "Haitong Liu, Qiang Li, Hoi-To Wai",
"categories": "math.OC",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a connection to SPDEs in continuously embedded spaces.
address:
- Ind... | arxiv_math | {
"id": "2309.03823",
"title": "A note on invariant manifolds for stochastic partial differential\n equations in the framework of the variational approach",
"authors": "Rajeev Bhaskaran and Stefan Tappe",
"categories": "math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
author:
- "Jingyu Gao[^1]"
- "Xiurui Geng[^2]"
title: "A linearly convergent method for solving high-order proximal operator[^3]"
---
[^1]: Aerospace Information Research Institute, Chinese Academy of Sciences; School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Science... | arxiv_math | {
"id": "2309.01306",
"title": "A linearly convergent method for solving high-order proximal operator",
"authors": "Jingyu Gao and Xiurui Geng",
"categories": "math.OC",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this article, we prove that every idempotent element of a $G$-graded commutative ring $R=\bigoplus\limits_{n\in G}R_{n}$ with $G$ an Abelian group is contained in the subring $\bigoplus\limits_{h\in H}R_{h}$ where $H$ is the torsion subgroup of $G$. This theorem gives an affirmative answer to the g... | arxiv_math | {
"id": "2309.02880",
"title": "Homogeneity of the Jacobson radical and idempotents in a graded ring",
"authors": "Abolfazl Tarizadeh",
"categories": "math.AC math.AG math.GR math.RA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We provide a different proof of the equivariant version of the Borsuk-Whitehead-Hanner Theorem in the category of proper $G$-spaces which are metrizable by a $G$-invariant metric.
author:
- |
Luis Martínez [^1]\
e-mail: luchomartinez9816\@hotmail.com\
Departamento de Matemáticas, Facultad de Cie... | arxiv_math | {
"id": "2309.16453",
"title": "A note on adjunction spaces and G-ANE's",
"authors": "Luis Mart\\'inez",
"categories": "math.GN",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0/"
} |
---
abstract: |
The compact 16-dimensional Moufang plane, also known as the Cayley plane, has traditionally been defined through the lens of octonionic geometry. In this study, we present a novel approach, demonstrating that the Cayley plane can be defined in an equally clean, straightforward and more economic way us... | arxiv_math | {
"id": "2309.00967",
"title": "A minimal and non-alternative realisation of the Cayley plane",
"authors": "Daniele Corradetti, Alessio Marrani, Francesco Zucconi",
"categories": "math.RA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We set out an elementary approach to derive Visible Point Identities summed on lattice points of inverted triangle (2D), pyramid (3D), hyperpyramid (4D, 5D and so on) utilizing the greatest common divisor for the nD Visible Point Vectors. This enables study of partitions in nD space into vector parts ... | arxiv_math | {
"id": "2309.16094",
"title": "Visible Point Vector Partition Identities for Hyperpyramid Lattices",
"authors": "Geoffrey B. Campbell",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
author:
- "David Gómez-Castro [^1]"
title: Beginner's guide to Aggregation-Diffusion Equations
---
[^1]: Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid. <dgcastro@ucm.es>
| arxiv_math | {
"id": "2309.13713",
"title": "Beginner's guide to Aggregation-Diffusion Equations",
"authors": "David G\\'omez-Castro",
"categories": "math.AP cs.NA math.NA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We analyze the spectrum of the Neumann-Poincaré (NP) operator for a doubly connected domain lying between two level curves defined by a conformal mapping, where the inner boundary of the domain is of general shape. The analysis relies on an infinite-matrix representation of the NP operator involving t... | arxiv_math | {
"id": "2309.02892",
"title": "Spectral analysis of the Neumann-Poincar\\'e operator for thin doubly\n connected domains",
"authors": "Doosung Choi and Mikyoung Lim and Stephen P. Shipman",
"categories": "math.SP math.FA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this paper, we examine the consistency of GCV for estimating the predict... | arxiv_math | {
"id": "2310.01374",
"title": "Corrected generalized cross-validation for finite ensembles of penalized\n estimators",
"authors": "Pierre Bellec, Jin-Hong Du, Takuya Koriyama, Pratik Patil, Kai Tan",
"categories": "math.ST stat.ME stat.ML stat.TH",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/... |
---
abstract: |
In this paper, we study a version of the Iitaka conjectures for anticanonical divisors over perfect fields of positive characteristic. That is, we prove the inequality $\kappa(X,-K_X)\leq \kappa(X_y,-K_{X_y})+\kappa(Y,-K_Y)$, for a contraction $f\colon X\rightarrow Y$ with general fibre $X_y$ having g... | arxiv_math | {
"id": "2309.16580",
"title": "Superadditivity of anticanonical Iitaka dimension for contractions with\n F-split fibres",
"authors": "Marta Benozzo, Iacopo Brivio, Chi-Kang Chang",
"categories": "math.AG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We construct the first example of a lattice on an irreducible Euclidean building that is not residually finite. Conjecturally, the normal subgroup theorem extends to this lattice making it virtually simple.
author:
- Thomas Titz Mite, Stefan Witzel
bibliography:
- reference.bib
date: October 2023
titl... | arxiv_math | {
"id": "2310.03662",
"title": "A C2-tilde-lattice that is not residually finite",
"authors": "Thomas Titz Mite, Stefan Witzel",
"categories": "math.GR",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
The main aim of this paper is to develop extreme value theory for $\theta$-expansions. We get the limit distribution of the largest value of $\theta$-continued fraction mixing stationary stochastic process and some related results. These are analogous to J.Galambos and W.Philipp theorems for the regul... | arxiv_math | {
"id": "2309.12654",
"title": "Some extreme value theory for $\\theta$-expansions",
"authors": "Gabriela Ileana Sebe and Dan Lascu",
"categories": "math.PR math.NT",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We construct a Hopf superalgebra structure for a Drinfeld super Yangian of Lie superalgebra $B(m,n)$ relative to all possible choices of Borel subalgebras. In order to do this we introduce a simplified definition of Drinfeld super Yangians.
address: MCCME (Moscow Center for Continuous Mathematical Edu... | arxiv_math | {
"id": "2309.09735",
"title": "Hopf superalgebra structure for Drinfeld super Yangian of Lie\n superalgebra $B(m,n)$",
"authors": "Alexander Mazurenko",
"categories": "math.QA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper we investigate the relation between Deddense and spectral radius algebras of two bounded linear operators that there is a similarity between them. Also, the Deddense and spectral radius algebras related to rank one operators, operators that are similar to a rank one operators, operators ... | arxiv_math | {
"id": "2310.05435",
"title": "On the Deddense algebras of a class of bounded operators",
"authors": "Z. Huang, Y. Estaremi and N. Shamsi",
"categories": "math.FA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
Connected graphs with a given dissociation number attaining the minimum spectral radius
Zejun Huang$^{1}$, Jiahui Liu$^{1}$[^1], Xinwei Zhang$^{1}$\
1. School of Mathematical Sciences, Shenzhen University, Shenzhen 518060, China \
**Abstract**
A dissociation set of a graph is a set of vertices which induces a subgra... | arxiv_math | {
"id": "2309.15597",
"title": "Connected graphs with a given dissociation number attaining the minimum\n spectral radius",
"authors": "Zejun Huang, Jiahui Liu, Xinwei Zhang",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Let $F$ be a $p$-adic field. For certain non-abelian nilpotent algebraic groups $U$ over $\bar\mathbb{Z}_p$ equipped with $\operatorname{Gal}_F$-action, we study the associated *Heisenberg varieties* which model the non-abelian cohomology set "$H^1(\operatorname{Gal}_F, U)$". The construction of Heise... | arxiv_math | {
"id": "2309.00761",
"title": "Heisenberg varieties and the existence of de Rham lifts",
"authors": "Zhongyipan Lin",
"categories": "math.NT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analyzed model equations suc... | arxiv_math | {
"id": "2309.02006",
"title": "Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order\n Interactions",
"authors": "Christian Bick, S\\\"oren von der Gracht",
"categories": "math.DS",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We represent by $\{W_{\lambda, t}^\alpha\}_{t>0}$ the semigroup generated by $-\mathbb L^{\alpha}_\lambda$, where $\mathbb L^{\alpha}_\lambda$ is a Hardy operator on a half space. The operator $\mathbb L^{\alpha}_\lambda$ includes a fractional Laplacian and it is defined by $$\mathbb L^{\alpha}_\lambd... | arxiv_math | {
"id": "2310.03540",
"title": "Variation operators associated with semigroups generated by Hardy\n operators involving fractional Laplacians in a half space",
"authors": "Jorge J. Betancor, Estefan\\'ia D. Dalmasso and Pablo Quijano",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/... |
---
abstract: |
Building on the work of Nozaki, Sato and Taniguchi, we develop an instanton-theoretic invariant aimed at studying strong corks and equivariant bounding. Our construction utilizes the Chern-Simons filtration and is qualitatively different from previous Floer-theoretic methods used to address these ques... | arxiv_math | {
"id": "2309.02309",
"title": "Involutions and the Chern-Simons filtration in instanton Floer homology",
"authors": "Antonio Alfieri, Irving Dai, Abhishek Mallick, Masaki Taniguchi",
"categories": "math.GT",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In 2009-2011 Pelayo and Vũ Ngọc classified semitoric integrable systems in terms of five invariants. Four of the invariants were already well-understood prior to the classification, but the fifth invariant, the so-called *twisting index invariant*, came as a surprise. Having a better understanding of ... | arxiv_math | {
"id": "2309.16614",
"title": "The twisting index in semitoric systems",
"authors": "Jaume Alonso, Sonja Hohloch, Joseph Palmer",
"categories": "math.SG math.DS",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Consider the elliptic operator given by $$\label{fx2}
\mathscr{L}_{\epsilon}f\,=\, \boldsymbol{b} \cdot \nabla f \,+\,
\epsilon\, \Delta f$$ for some smooth vector field ${\boldsymbol b}\colon {\mathbb R}^d\to{\mathbb R}^d$ and a small parameter $\epsilon>0$. Consider the initial-valued problem $$... | arxiv_math | {
"id": "2309.05546",
"title": "Metastability and time scales for parabolic equations with drift 1: the\n first time scale",
"authors": "Claudio Landim, Jungkyoung Lee, Insuk Seo",
"categories": "math.PR cond-mat.stat-mech math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper we demonstrate the first example of a finite translation plane which does not contain a translation hyperoval, disproving a conjecture of Cherowitzo. The counterexample is a semifield plane, specifically a Generalised Twisted Field plane, of order $64$. We also relate this non-existence ... | arxiv_math | {
"id": "2309.01451",
"title": "On Translation Hyperovals in Semifield Planes",
"authors": "Kevin Allen and John Sheekey",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
We introduce and begin the study of quasi-BPS categories for K3 surfaces, which are a categorical version of the BPS cohomologies for K3 surfaces.
We construct semiorthogonal decompositions of derived categories of coherent sheaves on moduli stacks of semistable objects on K3 surfaces, where each s... | arxiv_math | {
"id": "2309.08437",
"title": "Quasi-BPS categories for K3 surfaces",
"authors": "Tudor P\\u{a}durariu and Yukinobu Toda",
"categories": "math.AG",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
For a $\mathbb{Z}^{d}$-topological dynamical system $(X, T, \mathbb{Z}^d)$, an *isomomorphism* is a self-homeomorphism $\phi : X\to X$ such that for some matrix $M\in GL(d,\mathbb{Z})$ and any ${\bm n}\in \mathbb{Z}^{d}$, $\phi\circ T^{{\bm n}}=T^{M{\bm n}}\circ \phi$, where $T^{\bm n}$ denote the sel... | arxiv_math | {
"id": "2309.10156",
"title": "Large normalizers of ${\\mathbb Z}^{d}$-odometers systems and realization\n on substitutive subshifts",
"authors": "Christopher Cabezas and Samuel Petite",
"categories": "math.DS",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this short note, we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type: $$\Delta^{m}u=\sum_{l=0}^{m-1}\Delta^{l}\left\langle V_{l},du\right\rangle +\sum_{l=0}^{m-2}\Delta^{l}\delta\left(w_{l}du\right)+f\qquad \text{ in } B^{2m}\label{eq: Longue-Gastel syste... | arxiv_math | {
"id": "2309.13522",
"title": "Sharp Morrey regularity for an even order elliptic system",
"authors": "Chang-Yu Guo and Wen-Juan Qi",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung--Feller theorem. Both classes of permutations are counted by the Fuss--Catalan numbers. The study of one class leads to a generalization of results of Flajolet from cont... | arxiv_math | {
"id": "2310.06288",
"title": "Catalan-Spitzer permutations",
"authors": "Richard Ehrenborg, G\\'abor Hetyei and Margaret Readdy",
"categories": "math.CO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper we prove the local and global well-posedness of the time fractional abstract Schrödinger type evolution equation ($iD_t^\alpha u+Au+F(u)=0$) on the Hilbert space and as an application, we prove the local and global well-posedness of the fractional dispersive equation with static potentia... | arxiv_math | {
"id": "2309.08278",
"title": "On the fractional abstract Schrodinger type evolution equations on the\n Hilbert space and its applications to the fractional dispersive equations",
"authors": "Mingxuan He, Na Deng",
"categories": "math.AP",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
An important result in the theory of harmonic maps is due to Benoist--Hulin: given a quasi-isometry $f:X\to Y$ between pinched Hadamard manifolds, there exists a unique harmonic map at a finite distance from $f$. Here we show existence of harmonic maps under a weaker condition on $f$, that we call non... | arxiv_math | {
"id": "2310.05796",
"title": "Harmonic projections in negative curvature II: large convex sets",
"authors": "Ognjen To\\v{s}i\\'c",
"categories": "math.DG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
author:
-
- "Xin Guo[^1]"
- "Yufei Zhang[^2]"
bibliography:
- potential_game.bib
title: Towards An Analytical Framework for Potential Games
---
**Abstract.** Potential game is an emerging notion and framework for studying multi-agent games, especially with heterogeneous agents. Up to date, potential games have b... | arxiv_math | {
"id": "2310.02259",
"title": "Towards An Analytical Framework for Potential Games",
"authors": "Xin Guo, Yufei Zhang",
"categories": "math.OC cs.GT math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that is optimal for any observable. This complements earlier works of Cipolloni et. al. [@ETHpaper; @A2] and Benigni et. al. [@... | arxiv_math | {
"id": "2309.05488",
"title": "Eigenstate thermalisation at the edge for Wigner matrices",
"authors": "Giorgio Cipolloni, L\\'aszl\\'o Erd\\H{o}s, Joscha Henheik",
"categories": "math.PR math-ph math.MP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this paper we study a version of (non-Markovian) first passage percolation on graphs, where the transmission time between two connected vertices is non-iid, but increases by a *penalty factor* polynomial in their expected degrees. Based on the exponent of the penalty-polynomial, this makes it incre... | arxiv_math | {
"id": "2309.11880",
"title": "Four universal growth regimes in degree-dependent first passage\n percolation on spatial random graphs II",
"authors": "J\\'ulia Komj\\'athy, John Lapinskas, Johannes Lengler, Ulysse Schaller",
"categories": "math.PR cs.SI math.CO q-bio.PE",
"license": "http://arxiv.org/licens... |
---
abstract: |
We introduce the notion of Lie-Yamaguti algebra bundle, define its cohomology groups with coefficients in a representation and show that such bundles appeared naturally from geometric considerations in the work of M. Kikkawa, which motivates us to introduce this object in the proper mathematical frame... | arxiv_math | {
"id": "2309.05508",
"title": "Lie-Yamaguti Algebra Bundle",
"authors": "Saikat Goswami and Goutam Mukherjee",
"categories": "math.RA math.DG",
"license": "http://creativecommons.org/publicdomain/zero/1.0/"
} |
arxiv_math | {
"id": "2309.08383",
"title": "Dynamical Analysis of an Allelopathic Phytoplankton Model with Fear\n Effect",
"authors": "Shangming Chen, Fengde Chen, Vaibhava Srivastava and Rana D. Parshad",
"categories": "math.DS q-bio.PE",
"license": "http://creativecommons.org/licenses/by/4.0/"
} | |
---
abstract: |
The classical Maclaurin inequality asserts that the elementary symmetric means $$s_k(y) \coloneqq \frac{1}{\binom{n}{k}} \sum_{1 \leq i_1 < \dots < i_k \leq n} y_{i_1} \dots y_{i_k}$$ obey the inequality $s_\ell(y)^{1/\ell} \leq s_k(y)^{1/k}$ whenever $1 \leq k \leq \ell \leq n$ and $y = (y_1,\dots,y_... | arxiv_math | {
"id": "2310.05328",
"title": "A Maclaurin type inequality",
"authors": "Terence Tao",
"categories": "math.CA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We show the time decay of spherically symmetric Coulomb waves in $\mathbb R^{3}$ for the case of a repulsive charge. By means of a distorted Fourier transform adapted to $H=-\Delta+q\cdot |x|^{-1}$, with $q>0$, we explicitly compute the kernel of the evolution operator $e^{itH}$. A detailed analysis o... | arxiv_math | {
"id": "2309.01313",
"title": "$L^1\\rightarrow L^\\infty$ Dispersive estimates for Coulomb waves",
"authors": "Adam Black, Ebru Toprak, Bruno Vergara Biggio and Jiahua Zou",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0/"
} |
arxiv_math | {
"id": "2309.04052",
"title": "Riemannian Adaptive Regularized Newton Methods with H\\\"older Continuous\n Hessians",
"authors": "Chenyu Zhang and Rujun Jiang",
"categories": "math.OC",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} | |
---
abstract: |
This manuscript investigates the classical problem of determining conditions on the parameters $\alpha,\beta \in \mathbb{C}$ for which the integral transform $$C_{\alpha\beta}[\varphi](z):=\int_{0}^{z} \bigg(\frac{\varphi(\zeta)}{\zeta (1-\zeta)^{\beta}}\bigg)^\alpha\,d\zeta$$ is also univalent in the... | arxiv_math | {
"id": "2310.01965",
"title": "Univalence of horizontal shear of Ces\\`aro type transforms",
"authors": "Swadesh Kumar Sahoo and Sheetal Wankhede",
"categories": "math.CV",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which we refer to as a stratum based value function. We focus on semi... | arxiv_math | {
"id": "2309.16099",
"title": "Nonparametric estimation of a covariate-adjusted counterfactual\n treatment regimen response curve",
"authors": "Ashkan Ertefaie, Luke Duttweiler, Brent A. Johnson and Mark J. van der\n Laan",
"categories": "math.ST stat.ME stat.ML stat.TH",
"license": "http://creativecommons... |
---
abstract: |
This work focuses on regularity criteria of 3D generalized magneto-micropolar fluid system in terms of the pressure in Lorentz spaces inspired by the recent works in [@FS22] and [@LN22].
author:
- |
Jae-Myoung Kim$^{1}$\
$^{{\small 1}}$Department of Mathematics Education, Andong National Universit... | arxiv_math | {
"id": "2310.00217",
"title": "Regularity criteria of 3D generalized magneto-micropolar fluid system in\n terms of the pressure",
"authors": "Jae-Myoung Kim",
"categories": "math.AP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
author:
- |
Tahir Shamsher$^{a}$, S. Pirzada$^{b}$, Mushtaq A. Bhat$^{c}$\
$^{}$ *$^{a,b}$Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India*\
$^{}$*$^{c}$Department of Mathematics, National Institute of Technology, Srinagar, India*\
$^{a}$`tahir.maths.uok@gmail.com`; $^{b}$`pirzadas... | arxiv_math | {
"id": "2309.13252",
"title": "On the Estrada index of unicyclic and bicyclic signed graphs",
"authors": "Tahir Shamsher, S. Pirzada, Mushtaq A. Bhat",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0/"
} |
---
abstract: |
We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the value function under several sets of assumptions, and thus deri... | arxiv_math | {
"id": "2310.03181",
"title": "Stochastic optimal control in Hilbert spaces: $C^{1,1}$ regularity of\n the value function and optimal synthesis via viscosity solutions",
"authors": "Filippo de Feo and Andrzej \\'Swi\\k{e}ch and Lukas Wessels",
"categories": "math.OC math.AP math.PR",
"license": "http://crea... |
---
abstract: |
We introduce the concept of a Fock bundle, a smooth principal bundle over a surface equipped with a special kind of adjoint-valued 1-form, as a new tool for studying character varieties of surface groups. Although similar to Higgs bundles, the crucial difference is that no complex structure is fixed o... | arxiv_math | {
"id": "2310.04377",
"title": "Fock bundles and Hitchin components",
"authors": "Georgios Kydonakis, Charlie Reid, Alexander Thomas",
"categories": "math.DG math-ph math.GT math.MP",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
Hurwitz numbers enumerate branched morphisms between Riemannn surfaces with fixed numerical data. They represent important objects in enumerative geometry that are accessible by combinatorial techniques. In the past decade, many variants of Hurwitz numbers have appeared in the literature. In this pape... | arxiv_math | {
"id": "2310.05225",
"title": "Combinatorics of pruned Hurwitz numbers",
"authors": "Sean Gearoid Fitzgerald, Marvin Anas Hahn, S\\'iofra Kelly",
"categories": "math.CO math.AG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
The classification of the maximal subgroups of the Monster $\mathbf{M}$ is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that $\mathbf{M}$ has no maximal subgroups that are almost simple with socle isomorphic to ${\rm PSL}_2(8)$, ${\rm PSL}_2(16)$, or ${\rm PS... | arxiv_math | {
"id": "2310.03317",
"title": "Indeed, the Monster has no almost simple maximal subgroup with socle\n $\\text{PSL}_2(16)$",
"authors": "Heiko Dietrich, Melissa Lee, Tomasz Popiel",
"categories": "math.GR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
A CUR factorization is often utilized as a substitute for the singular value decomposition (SVD), especially when a concrete interpretation of the singular vectors is challenging. Moreover, if the original data matrix possesses properties like nonnegativity and sparsity, a CUR decomposition can better... | arxiv_math | {
"id": "2310.00636",
"title": "A DEIM-CUR factorization with iterative SVDs",
"authors": "Perfect Y. Gidisu and Michiel E. Hochstenbach",
"categories": "math.NA cs.NA",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
# Introduction
Reaction-diffusion equations have been used to study a wide range of phenomena within the natural sciences, and are a topic of great mathematical intrigue in their own right. They appear as models for the spread of populations [@fisher1937wave; @kolmogorov1937etude; @aronson1978multidimensional], phase ... | arxiv_math | {
"id": "2309.13899",
"title": "Branching stable processes and motion by mean curvature flow",
"authors": "Kimberly Becker, Alison Etheridge, Ian Letter",
"categories": "math.PR",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We consider products of matrices of the form $A_n=O_n+\epsilon N_n$ where $O_n$ is a sequence of $d\times d$ orthogonal matrices and $N_n$ has independent standard normal entries and the $(N_n)$ are mutually independent. We study the Lyapunov exponents of the cocycle as a function of $\epsilon$, givin... | arxiv_math | {
"id": "2309.08193",
"title": "Lyapunov exponents of orthogonal-plus-normal cocycles",
"authors": "Sam Bednarski and Anthony Quas",
"categories": "math.DS",
"license": "http://creativecommons.org/licenses/by-sa/4.0/"
} |
---
abstract: |
Mosconi [@mosconi2021] proved Liouville theorems for ancient solutions of subexponential growth to the heat equation on a manifold with Ricci curvature bounded below. We extend these results to graphs with bounded geometry: for a graph with bounded geometry, any nonnegative ancient solution of subexpo... | arxiv_math | {
"id": "2309.17250",
"title": "Liouville theorems for ancient solutions of subexponential growth to the\n heat equation on graphs",
"authors": "Bobo Hua and Wenhao Yang",
"categories": "math.DG math.MG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We discuss two variations of Edwards' duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particular, we allow the functions in the cone to have a non-empty common zero set. In the second variation, we replace suprema of ... | arxiv_math | {
"id": "2309.12762",
"title": "Variations on a theorem by Edwards",
"authors": "M{\\aa}rten Nilsson and Frank Wikstr\\\"om",
"categories": "math.CV",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uni... | arxiv_math | {
"id": "2309.11410",
"title": "Equilibrium measures for two-sided shift spaces via dimension theory",
"authors": "Vaughn Climenhaga, Jason Day",
"categories": "math.DS",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this note, we prove the quantitative observability with an explicit control cost for the 1D Schrödinger equation over ${\mathbb{R} }$ with real-valued, bounded continuous potential on thick sets. Our proof relies on different techniques for low-frequency and high-frequency estimates. In particular,... | arxiv_math | {
"id": "2309.00963",
"title": "Quantitative observability for one-dimensional Schr\\\"odinger equations\n with potentials",
"authors": "Pei Su, Chenmin Sun, Xu Yuan",
"categories": "math.AP math.OC",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this note, we discuss and motivate the use of the terminology "median graphs" in place of "CAT(0) cube complexes" in geometric group theory.
author:
- Anthony Genevois
bibliography:
- CCvsMedian.bib
title: Why CAT(0) cube complexes should be replaced with median graphs
---
A *CAT(0) cube complex* ... | arxiv_math | {
"id": "2309.02070",
"title": "Why CAT(0) cube complexes should be replaced with median graphs",
"authors": "Anthony Genevois",
"categories": "math.GR math.MG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We prove that $3$-dimensional ellipsoids invariant under a $2$-torus action contain infinitely many distinct immersed minimal tori, with at most one exception. These minimal tori bifurcate from the $2$-torus orbit of largest volume at a dense set of eccentricities, and remain invariant under a circle.... | arxiv_math | {
"id": "2309.13758",
"title": "Bifurcations of Clifford tori in ellipsoids",
"authors": "Renato G. Bettiol, Paolo Piccione",
"categories": "math.DG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We construct a divergence-free velocity field $u:[0,T] \times \mathbb{T}^2 \to \mathbb{R}^2$ satisfying $$u \in C^\infty([0,T];C^\alpha(\mathbb{T}^2)) \quad \forall \alpha \in [0,1)$$ such that the corresponding drift-diffusion equation exhibits anomalous dissipation for every smooth initial data. We ... | arxiv_math | {
"id": "2309.08576",
"title": "Norm Growth, Non-uniqueness, and Anomalous Dissipation in Passive\n Scalars",
"authors": "Tarek M. Elgindi and Kyle Liss",
"categories": "math.AP physics.flu-dyn",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
The directed Oberwolfach problem OP$^\ast(m_1,\ldots,m_k)$ asks whether the complete symmetric digraph $K_n^\ast$, assuming $n=m_1+\ldots +m_k$, admits a decomposition into spanning subdigraphs, each a disjoint union of $k$ directed cycles of lengths $m_1,\ldots,m_k$. We hereby describe a method for c... | arxiv_math | {
"id": "2309.12549",
"title": "The directed Oberwolfach problem with variable cycle lengths: a\n recursive construction",
"authors": "Suzan Kadri and Mateja \\v{S}ajna",
"categories": "math.CO",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
---
abstract: |
In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply that the subgroup topology is not discrete. We mention various c... | arxiv_math | {
"id": "2309.08400",
"title": "About discrete subgroups of full groups of measure preserving\n equivalence relations",
"authors": "Vadim Alekseev, Alessandro Carderi, Andreas Thom, and Robin\n Tucker-Drob",
"categories": "math.GR math.DS",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We initiate the study of the spectrum $\mathop{\mathrm{Vspec}}(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in the sense that if $\mathbf T$ and $\mathbf T'$ are club-isomorphic, then $V(\mathbf T)\mathbi... | arxiv_math | {
"id": "2309.03821",
"title": "The vanishing levels of a tree",
"authors": "Assaf Rinot, Shira Yadai, Zhixing You",
"categories": "math.LO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
The alpha complex is a fundamental data structure from computational geometry, which encodes the topological type of a union of balls $B(x;r) \subset \mathbb{R}^m$ for $x\in S$, including a weighted version that allows for varying radii. It consists of the collection of "simplices" $\sigma=\{x_0,...,x... | arxiv_math | {
"id": "2310.00536",
"title": "Computing the alpha complex using dual active set methods",
"authors": "Erik Carlsson, John Carlsson",
"categories": "math.AT cs.CG",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
For each integer $k>0$, let $n_k$ and $m_k$ be integers such that $n_k\geq 2, m_k\geq 2$, and let $\mathcal{D}_k$ be a subset of $\{0,\dots,n_k-1\}\times
\{0,\dots,m_k-1\}$. For each $w=(i,j)\in \mathcal{D}_k$, we define an affine transformation on $\mathbb{R}^2$ by $$\label{eq:Sk}
\Psi_w(x)=\Ph... | arxiv_math | {
"id": "2309.08148",
"title": "Multifractal analysis of a class of self-affine Moran sets",
"authors": "Yifei Gu, Chuanyan Hou, Jun Jie Miao",
"categories": "math.CA",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
We provide a complete characterization of theories of tracial von Neumann algebras that admit quantifier elimination. We also show that the theory of a separable tracial von Neumann algebra $\mathcal{N}$ is never model complete if its direct integral decomposition contains $\mathrm{II}_1$ factors $\ma... | arxiv_math | {
"id": "2310.06197",
"title": "Quantum Expanders and Quantifier Reduction for Tracial von Neumann\n Algebras",
"authors": "Ilijas Farah, David Jekel, Jennifer Pi",
"categories": "math.OA math.LO",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
} |
---
abstract: |
In this paper we analyze the probability distributions associated with rolling (possibly unfair) dice infinitely often. Specifically, given a $q$-sided die, if $x_i\in\{0,\ldots,q-1\}$ denotes the outcome of the $i^{\text{th}}$ toss, then the distribution function is $F(x)=\mathbb{P}[X\leq x]$, where ... | arxiv_math | {
"id": "2309.07366",
"title": "Induced Distributions from Generalized Unfair Dice",
"authors": "Douglas T. Pfeffer, J. Darby Smith, and William Severa",
"categories": "math.PR",
"license": "http://creativecommons.org/licenses/by/4.0/"
} |
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